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Activity Number: 506
Type: Invited
Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #307293
Title: Minimax Bounds for Sparse PCA with Noisy High-Dimensional Data
Author(s): Iain M. Johnstone*+
Companies: Stanford University
Keywords: Principal components analysis ; eigenvector ; sparsity ; lower bound ; covariance matrix

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the quadratic loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk points to the existence of different regimes of sparsity of the eigenvectors. We also propose a new method for estimating the eigenvectors by a two-stage coordinate selection scheme. Joint work with Aharon Birnbaum, Boaz Nadler and Debashis Paul.

Authors who are presenting talks have a * after their name.

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